Optimal reactive nitrogen control pathways identified for cost-effective PM2.5 mitigation in Europe

Excess reactive nitrogen (Nr), including nitrogen oxides (NOx) and ammonia (NH3), contributes strongly to fine particulate matter (PM2.5) air pollution in Europe, posing challenges to public health. Designing cost-effective Nr control roadmaps for PM2.5 mitigation requires considering both mitigation efficiencies and implementation costs. Here we identify optimal Nr control pathways for Europe by integrating emission estimations, air quality modeling, exposure-mortality modeling, Nr control experiments and cost data. We find that phasing out Nr emissions would reduce PM2.5 by 2.3 ± 1.2 μg·m−3 in Europe, helping many locations achieve the World Health Organization (WHO) guidelines and reducing PM2.5-related premature deaths by almost 100 thousand in 2015. Low-ambition NH3 controls have similar PM2.5 mitigation efficiencies as NOx in Eastern Europe, but are less effective in Western Europe until reductions exceed 40%. The efficiency for NH3 controls increases at high-ambition reductions while NOx slightly decreases. When costs are considered, strategies for both regions uniformly shift in favor of NH3 controls, as NH3 controls up to 50% remain 5-11 times more cost-effective than NOx per unit PM2.5 reduction, emphasizing the priority of NH3 control policies for Europe.

Ambient PM 2.5 (fine particulate matter with an aerodynamic diameter ≤2.5 µm) air pollution is one of the leading risk factors for premature mortalities worldwide, according to the Global Burden of Disease (GBD) study 1 , responsible for millions of deaths and lost years of healthy life annually in recent years [1][2][3] . Long-term policies for PM 2.5 mitigation have been implemented in many countries and have effectively reduced PM 2.5 concentrations [4][5][6][7] . However, large numbers of people are still exposed to harmful PM 2.5 levels even in places with relatively clean ambient air such as Europe 7 ; 59% of European stations exceed the World Health Organization (WHO) guideline for the PM 2.5 annual mean (10 μg·m −3 ) in 2019 8 . Recent epidemiological studies also demonstrated that PM 2.5 air pollution can affect human health at very low levels 9,10 . The WHO thus released an updated guideline value for PM 2.5 annual mean concentrations (5 μg·m −3 ) 3 , which was exceeded at 97% of European monitoring stations in 2019 8 . This poses a tremendous challenge for cleaning up European air as much more stringent mitigation measures will be needed to achieve such an ambitious goal. The WHO also suggested interim targets to be considered, although recognizing that interim targets are insufficient to remove adverse health impacts.
Excess reactive nitrogen (Nr), including nitrogen oxides (NO x = NO + NO 2 ), ammonia (NH 3 ), nitrate (NO 3 − ), and ammonium (NH 4 + ) are recognized environmental threats to ecosystems, deteriorating the quality of air, soil, and water 11,12 . Anthropogenic Nr sources have dramatically increased since 1960 13 , exacerbating the global nitrogen cycle and consequent damaging effects on human health and ecosystems 13,14 . Capping anthropogenic Nr emissions (mainly NO x and NH 3 ) is a high priority for environmental protection 15,16 . In particular, Nr controls benefit PM 2.5 mitigation because both NO x and NH 3 are precursors of secondary inorganic aerosols (SIAs, including sulfate, nitrate, and ammonium) components in PM 2.5 , apart from sulfur dioxide (SO 2 ) 14,17,18 . SIAs strongly contribute to the PM 2.5 mass concentrations in Europe [19][20][21] , contributing above 50% of total annual PM 2.5 mass concentrations in parts of Europe, i.e., Germany, the Netherlands, and Belgium [22][23][24] . Atmospheric abundance of NH 3 and NO x gases determine the formation of SIAs, and effectiveness of PM 2.5 mitigation from Nr controls [25][26][27] . NH 3 preferably reacts with sulfuric acid (H 2 SO 4 , produced by the oxidation of SO 2 ) to form ammonium sulfate aerosol, and with more NH 3 available, further reacts with nitric acid (HNO 3 , produced by the oxidation of NO x ) to form ammonium nitrate aerosol.
The revised Gothenburg Protocol has set national Nr emission ceilings for 2020, i.e., 42% NO x emission reductions and 6% NH 3 emission reductions in 2020 relative to 2005 for the European Union (EU) 28 and other participating countries. The National Emissions Ceiling Directive further establishes national Nr emission reduction targets in 2030, i.e., 63% NO x emission reductions and 19% NH 3 emission reductions in 2030 relative to 2005 in the EU 29 . All existing national targets show more ambitious controls for NO x than NH 3 . Most countries have not prioritized limiting NH 3 emissions in part due to uncertainties in NH 3 sources and concerns about its control effectiveness for PM 2.5 mitigation, in addition to food security concerns 17 , with agriculture being the dominant source of NH 3 . However, recent studies found agricultural (mainly NH 3 ) emissions make the largest relative contribution to PM 2.5 mortality in Europe among all sources 2,30,31 . Gu et al. 18 also found that the cost of 50% NH 3 emissions abatement is much less than that of NO x emissions globally. However, the priority for NO x or NH 3 emission reductions to meet the updated WHO guideline and zero pollution action plan 32 in Europe remains uncertain.
In this study, we quantify the contribution and efficiency of Nr emission reductions for PM 2.5 mitigation in Europe for 2015 and derive the optimal pathway for Nr emission controls. We use recent European emission estimates, a regional air quality model, the newly developed exposure mortality model, Nr control scenarios, and emission control costs to systematically analyse the impact of Nr emission controls on PM 2.5 air pollution (Methods). We demonstrate that Nr emission controls can reduce PM 2.5 concentrations, PM 2.5 -related health impacts, and help achieve the WHO guideline in Europe. The optimal pathway targeting PM 2.5 abatement changes towards prioritizing NH 3 measures after considering control costs, indicating NH 3 emission reductions are the most cost-effective way to combat European PM 2.5 air pollution.

Results and discussion
The contribution of Nr emissions on PM 2.5 air pollution Our ECLIPSE inventory derived from the GAINS (Greenhouse gas and Air pollution Interactions and Synergies) model (Methods) estimates the total anthropogenic NO 2 and NH 3 emissions over Europe in 2015 to be 3.7 Tg N and 4.4 Tg N, respectively, which are comparable to other emission inventories (Supplementary Table 1). Considering monthly time factors, NH 3 emissions tend to peak during the warm season (April-September), while NO x emissions peak during the cold season in Europe. Such seasonality appears stronger in our estimates than in the EDGAR and EMEP inventories ( Supplementary Fig. 1). Both NH 3 and NO x emissions are higher in the western part of Europe than in the east. This ECLIPSE emissions inventory is used as an input to the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) regional air quality model to assess the impacts of Nr emission reductions on PM 2.5 air pollution in Europe. A series of WRF-Chem simulations are conducted over Europe for the representative months (January, April, July, and October) in 2015 (Methods). The baseline simulation in Europe, after improving simulated organic carbon (OC) and dust by matching observations of PM 2.5 components (Supplementary Figs 2 and 3), well captures measured surface PM 2.5 concentrations with the correlation coefficients (R) > 0.59 and mean bias (MB) < −6% ( Supplementary Fig. 3). The magnitudes and variations of the observed SIAs concentrations are generally captured by the baseline simulation, except in summer, when the model underestimates nighttime nitrate volatility and overestimates nitrate concentrations. The simulated surface annual NH 3 concentrations are also in good agreement with measurements in Europe with R = 0.92 and MB of within −3% (Supplementary Fig. 4).
The contribution of anthropogenic Nr emissions to PM 2.5 air pollution can be calculated as the difference between the baseline simulation and a sensitivity simulation with anthropogenic Nr emissions set to zero (Methods). Figure 1 shows that the reduction in regional annual mean PM 2.5 concentrations when phasing out anthropogenic Nr emissions is 2.3 ± 1.2 μg·m −3 (mean ± standard deviation) in Europe for 2015. The response to such emission controls for PM 2.5 concentrations is stronger in Western Europe than in Eastern Europe, with the largest effects occurring in the Netherlands, Belgium and northern Germany. For evaluation, we separate Europe into Western Europe and Eastern Europe along country borders, guided by the spatial difference of PM 2.5 changes from Nr emission controls (the thick black line in Fig. 1). We further apply a metric of N-share 18 to quantify the contribution of Nr compounds to total PM 2.5 concentrations, which is defined as the relative change in model simulated PM 2.5 concentrations with vs. without anthropogenic Nr emissions. The N-share caused by anthropogenic Nr emissions contributes about 29% (range, 17-31%) to PM 2.5 pollution in Western Europe and 12% (8.7-16%) in Eastern Europe for 2015, exceeding 50% in some parts of Western Europe. The N-shares of NH 3 emissions are larger than those of NO x emissions and close to the N-shares of total Nr emissions because the NH 3 reductions curtail both contributions of NO x and SO 2 to SIAs formation, which is in agreement with results of Gu et al. 18 .
Nr abatement would help Europe to achieve the limit set in the updated WHO guidelines for PM 2.5 concentrations and substantially mitigate PM 2.5 -related health burdens. In 2015, only 14% of Western Europe met the PM 2.5 annual mean <5 μg·m −3 (the updated WHO guideline value) and all of Eastern Europe exceeded this guideline level. Figure 2 shows that phasing out Nr emissions prompt an additional 28% of Western Europe to achieve the guideline value for annual mean PM 2.5 . NH 3 emission controls render twice as much area in Western Europe meeting the guideline value compared to similar strengths of NO x emission controls. However, annual mean PM 2.5 concentrations in Eastern Europe cannot reach this guideline value with Nr abatement alone and need to reduce emissions of other PM 2.5 precursors. In addition, Western Europe and Eastern Europe have 18% and 38% of all days in 2015 exceeding the guideline value for the daily average PM 2.5 , and Nr abatement cuts the daily exceedance by 41% and 16% respectively. The Global Exposure Mortality Model (GEMM) is then applied to assess PM 2.5 -related chronic health impacts (Methods). We further find setting anthropogenic Nr emissions to zero could avoid 99,000 (95% confidence interval: 92,000-106,000) PM 2.5 -related premature deaths in Europe in 2015, decreasing the annual PM 2.5 -related mortality by 29% and 6% in Western Europe and Eastern Europe, respectively ( Supplementary Fig. 5).

The efficiency of Nr emission reductions in Europe
The analyses above illustrate a larger contribution of NH 3 emissions to PM 2.5 concentrations, and that phasing out NH 3 emissions leads to larger areas and more days meeting the updated WHO guideline value for PM 2.5 air pollution compared to phasing out NO x . We further investigate the effectiveness of Nr emission controls under different reduction levels in sensitivity simulations with NH 3 and NO x emission reductions of 0%, 30%, 60%, 80%, and 100% over Europe in 2015 (Methods). We should note such reduction strengths extend to very drastic changes of atmospheric conditions that, while currently not seeming realistic, guide the way towards conditions compatible with the WHO guideline values and provide the information needed to devise efficient abatement. Figure 3 shows changes in regional mean PM 2.5 concentrations and related premature deaths in Western Europe and Eastern Europe as anthropogenic Nr emissions are gradually reduced. In Western Europe, the PM 2.5 concentrations decline non-linearly following NH 3 emission reductions, resulting in modest PM 2.5 changes with limited NH 3 emission reductions, which is similar to the response found in China 26 . The regional mean PM 2.5 concentrations in Western Europe for 2015 would decrease by 0.40 ± 0.15/1.03 ± 0.41/2.51 ± 1.06 μg·m -3 with 30%/60%/100% NH 3 emission reductions in Europe. Only a deep NH 3 abatement (up to about 80%) would yield larger total PM 2.5 decreases  required to meet the WHO AQG for annual mean PM 2.5 (5 μg·m −3 ). Blue, red, and black lines in (a) represent changes of regional mean daily PM 2.5 exceedance in Western Europe, Eastern Europe, and all Europe, respectively. Gray areas in (b), (c), and (d) represent locations where even 100% Nr emission controls cannot lead to achievement.
in Western Europe than the same level of NO x abatement. We note a difference to previous studies 33,34 that expect higher efficiency for NH 3 already at a much lower level of abatement, which we understand to be the result of a change in the chemical regime since these earlier studies were performed. While PM 2.5 decreases in Eastern Europe associated with NH 3 emission reductions tend to be more linear than those in Western Europe, the responses are similar to NO x emission reductions. Notably, during summer, both regions exhibit a more linear relationship between PM 2.5 concentrations and NH 3 emission reductions, primarily due to the greater availability of HNO 3 compared to other seasons ( Supplementary Fig. 6). Meanwhile, we find stronger nonlinear responses on PM 2.5 -related premature deaths in both regions due to the non-linear relationship between health risk and PM 2.5 exposure; their values can be decreased by 8.7 (8.0-9.3)/24 (22-26)/72 (67-78) thousands PM 2.5 -related premature deaths in Western Europe for 2015 when NH 3 emissions are reduced by 30%/60%/100%.
We quantify the effectiveness for PM 2.5 reductions by calculating the instant efficiency of Nr emission controls (β, Methods). β Nr /β NOx / β NH3 estimates the instant response of total PM 2.5 mass in percent for each 1% mass reduction in Nr/NO x /NH 3 emissions. As shown in Fig. 3, the regional mean β NH3 increases rapidly while β NOx slowly decreases as the level of emission reduction rises. Under the 2015 emission condition, the β NH3 efficiencies in Western Europe increase from 0.12 ± 0.05%/% in the base condition to 0.48 ± 0.33%/% (a factor of 4 higher) when NH 3 emissions are reduced by 80%, while the β NOx efficiencies decrease from 0.25 ± 0.13%/% to 0.14 ± 0.07%/%. The efficiencies in Eastern Europe are less than half of those in Western Europe due to the higher PM 2.5 concentrations and lower N-share ( Fig. 1), and are less sensitive to Nr emission changes.
We then apply the chemical regime metric of G ratio 25 to explain the changes in the instant efficiency associated with NH 3 emission controls. The G ratio denotes the ratio between free ammonia (NH 3 and NH 4 + ) and total nitrate (HNO 3 + NO 3 − ) after neutralization of H 2 SO 4 (note, all the terms are expressed on a molar basis, Methods). The 2015 mean G ratio is found to be almost always above 1 across Europe (4.5 ± 2.4 in Western Europe and 2.8 ± 1.7 in Eastern Europe), indicating a HNO 3 -limited chemical regime and causing the SIAs formation to be more sensitive to small changes in NO x emissions than those in NH 3 emissions ( Supplementary Fig. 7). This phenomenon is particularly evident in April (with a G ratio of 6.3 ± 3.2 in Western Europe and 4.2 ± 2.0 in Eastern Europe) due to the high ammonia emissions occurring in Europe during this month. In contrast, the G ratio is close to 1 in most of Eastern Europe for January, July, and October, when NH 3 controls are slightly more efficient than NO x controls ( Supplementary  Fig. 6). The G ratio decreases as we gradually reduce NH 3 emissions and Europe shifts to the NH 3 -limited chemical regime, leading to NH 3 abatement becoming increasingly effective ( Supplementary Fig. 8). When we gradually reduce NO x emissions, Europe remains in the HNO 3 -limited chemical regime but the β NOx decreases due to decreases in oxidants ( Supplementary Figs. 8 and 9). Changes in β Nr depend on both β NOx changes and shifts in the chemical regime. This results in a slow decrease of β Nr in Western Europe and a trend of first decreasing b a d c and then increasing in Eastern Europe with deeper emission reductions.
A tipping point for the Nr controls can be identified where the PM 2.5 response from NH 3 emission reductions outweighs that from NO x emission reductions, i.e., by interpolating β NH3 −β NOx or G−1 to reach zero among a series of NH 3 and NO x abatement sensitivity tests (Methods). We find that the β NH3 −β NOx tends to be positive as Nr emissions are reduced, and it has larger changes in the places with more excessive NH 3 (Supplementary Fig. 10). Figure 4 shows the tipping point of Nr emission reductions for instant efficiencies are 36% ± 16% and 18% ± 22% in Western Europe and Eastern Europe, respectively. It indicates small mitigation for NH 3 or NO x can decrease the same PM 2.5 concentrations in Western Europe after around 36% emission reductions in 2015. However, the G ratios are still above 1 under these abatement scenarios, and the tipping point for G ratio = 1 needs a deeper NH 3 abatement (73% ± 16% in Western Europe and 46% ± 24% in Eastern Europe). The discrepancies between metrics of the chemical regime for SIAs formation and the effectiveness for PM 2.5 decreases are also found in Thunis et al. 35 .
We find the first explanation for the discrepancy between the tipping point from β efficiency and that from the G ratio would be the different unit of Nr abatement, the former indicating the same PM 2.5 decreases with per 1% mass reduction of Nr emissions and the latter indicating per unit mole reduction. This discrepancy is reduced by 36-41% when we transfer the unit of β from mass-based to molarbased. The residual discrepancy can be explained by their different definitions and applicable targets. The G ratio is based on a homogeneous air parcel at any specific moment and it loses extreme values when applied to the regional air quality model. As shown in Fig. 4, the tipping point for the G ratio falls rapidly with height while β changes steadily. Therefore, the decrease of surface PM 2.5 depends on the chemical regime of each specific grid cell and time interval. This demonstrates that the instant efficiency is more suitable for evaluating Nr emission controls for PM 2.5 mitigation while the chemical regime only provides a rough direction.

The optimal pathway for Nr abatement in Europe
Here, we develop and apply a diagnostic diagram for the effectiveness of PM 2.5 abatement to find the optimal pathway of Nr emission controls in Europe (Methods). It visualizes the regional mean PM 2.5 reductions as isopleths and the combined instant efficiency for PM 2.5 abatement (the gradient) as arrows. As shown in Fig. 5, the gradient in Western Europe for the 2015 base condition tends to shift towards NO x , which indicates that NO x emission controls would initially be most effective. By contrast, for Eastern Europe NH 3 and NO x emission controls have the similar effects in the early stage. Following the direction of gradients, we find that the optimal pathway of Nr emission controls in Western Europe entails always stronger reductions in NO x than NH 3 emissions so that the regional mean PM 2.5 concentrations decline the fastest. This pathway approaches to reductions of~100% NO x emissions and 40% NH 3 emissions inducing PM 2.5 decreases by 2.2-2.4 μg·m −3 , and further NH 3 emission reductions will lead to an additional 0.4 μg·m −3 decrease. In contrast, the optimal pathway of Nr emission controls in Eastern Europe shall have a deeper NH 3 abatement where~100% NH 3 and 60% NO x emission reductions result in PM 2.5 decreases by 1.7-1.9 μg·m -3 .
In addition to PM 2.5 abatement, cost considerations are also essential information for policy-making. Here we note that the optimal pathway of Nr emission controls changes uniformly in favor of NH 3 emission reductions when we consider control costs. We quantify Nr emission abatement technologies and related costs (including investment costs, fixed and operating costs) according to the GAINS model [36][37][38] . Figure 5 shows the annual total costs for Nr abatement in Western Europe and Eastern Europe according to integration and interpolation among five sets of feasible emission control scenarios at the national level reported by Amann et al. 39 . Here, the costs refer to the extra annual costs incurred by the individual abatement measures to reduce Nr emissions. The abatement measures for NO x emissions stem mainly from the power and industrial sectors, while those for NH 3 are mainly from agricultural livestock farming and fertilizer use. We find NH 3 emission controls are always cheaper than NO x emission controls and Western Europe has higher costs to control Nr emissions than Eastern Europe due to the reduction policies already in place and higher levels of Nr emissions. Currently feasible emission abatement technologies in the GAINS model can reduce NO x and NH 3 emissions by 16% and 29% in Western Europe, annually costing 3.7 and 0.8 billion euros, respectively; reduce NO x and NH 3 emissions by 32% and 31% in Eastern Europe, annually costing 1.9 and 0.2 billion euros, respectively.
We further update the diagnostic diagram of cost-effectiveness using the ratio of control costs and PM 2.5 abatement, which denotes the annual costs per unit PM 2.5 decreases (Fig. 5). Due to the limited availability of cost data for high abatement levels, we merely extrapolate to 50% emission reductions. In Western Europe, controlling 10% (30%) NH 3 emissions from the 2015 Base would decrease regional PM 2.5 by 0.11 (0.40) μg m −3 and require implementation costs of 0.08 (1.1) billion euros. In comparison, controlling 10% (30%) NO x emissions there would decrease regional PM 2.5 by 0.23 (0.67) μg m −3 with implementation costs of 1.1 (12.7) billion euros. Similar cost-effective NH 3 emission controls can be seen in Eastern Europe. The optimal pathway of cost-effective Nr emission controls follows the lowest isopleths for the cost/PM 2.5 abatement ratio, inferring NH 3 emission reductions only in both Western Europe and Eastern Europe. The much lower cost and increasing efficiency of NH 3 emission control diminish the need for NO x emission control.
Nr emission controls thus can help Europe towards achieving the updated WHO guideline value, reducing PM 2.5 air pollution by 12-29% and PM 2.5 -related mortality by 6-29% in Europe in 2015. Eastern Europe (G ratios of 1-5) represents an area slightly in excess of NH 3 where modest NO x or NH 3 emission reductions abate similar PM 2.5 concentrations. In contrast, Western Europe (G ratios of 2-7) represents a highly NH 3 -excessive area where PM 2.5 abatement does not become effective until NH 3 reduction reaches above 40%. When considering control costs, the optimal pathway for halving Nr emissions clearly points towards NH 3 management. Policy challenges specific to NH 3 abatement have been described recently by Gu et al. 40 . Identifying the optimal pathway for Nr emission reductions combining the effectiveness of PM 2.5 abatement and emission control costs may also be important in many other regions over the globe, such as China, India, and the United States, where nitrogen pollution has continued to grow in recent years [41][42][43] . These regions are also facing heavy loads of PM 2.5 air pollution and challenges to meet the updated WHO guideline value 7,44 . In addition to the benefits for PM 2.5 mitigation and human health, Nr emission controls can also help reduce nitrogen deposition and surface ozone ( Supplementary Fig. 9), which should be integrally considered in environmental strategies in future work.
In closing, we note that some uncertainties are associated with our analyses. First, several emission inventories based on different sectoral categories and collected by different institutions provide a considerable range of Nr emission estimates in Europe. While the estimates we use are within the range (Supplementary Table 1), the net results will be affected by the choice of Nr input. Second, the availability of NH 3 may significantly elevate the aerosol water content and alkalinity and then enhance the production of SIAs and SOA 45,46 . The contribution of NH 3 emissions on PM 2.5 air pollution would thus present a lower estimate only, as here, the alkalinity is limited to the heterogeneous production of SIAs, and the SOA formation is parameterised as a multiple of OC concentrations. Furthermore, our study has not included the bidirectional exchange of NH 3 , i.e., simultaneous fluxes from and deposition to agricultural areas, which is highly uncertain and may alter the effectiveness of PM 2.5 mitigation 47,48 .

Observations of air pollutants and meteorology
Daily and hourly surface chemical measurements in Europe in 2015 are obtained from the air quality database of the European Environment Agency (EEA). We use 964 background stations for PM 2.5 , which are then spatially aggregated into 565 grid cells to get a more representative evaluation of the model results. In addition, we use 27 stations for BC, 30 stations for OC, 34 stations for SIAs (Supplementary  Table 2 Table 3).
The WRF-Chem model Step Time-Split Euler Method in the gas-particle partitioning module of MOSAIC 52 . We add the heterogeneous sulfate formation reactions on particle surfaces based on Chen et al. 53 to improve SIAs simulation. The Rapid Radiative Transfer Model for GCMs (RRTGM) scheme is used to parameterize shortwave and longwave radiation transfer 54 . Other physical parameterizations are the same as those used by Liu et al. 26 .
Model improvement. Our model will underestimate PM 2.5 concentrations as the chemical mechanisms do not consider online secondary organic aerosol (SOA) formation due to its high uncertainty.
Here we use a multiple of the OC concentrations to make up the SOA component by comparing simulated PM 2.5 components to the observations ( Supplementary Fig. 2). SOA concentrations are characterized as three times that of OC in summer and two times in other months 55 . This SOA assumption has little effect on our results because SIA and SOA chemistry are decoupled in the model. In addition, to account for OC underestimates, we increase the OC concentrations in Eastern and Central European countries by two and five times, respectively.

Model sensitivity simulations.
We conduct a Base simulation in 2015 and a series of sensitivity simulations to examine the impacts of Nr emission reductions on PM 2.5 air quality in Europe. First, the baseline simulation (denoted as Base) incorporates the 2015 emissions described above that have been assessed using observations. Second, a group of sensitivity simulations (denoted as S1RN, N = 30, 60, 80, and 100) reduces anthropogenic Nr emissions (both NO x and NH 3 emissions) over Europe by 30%, 60%, 80%, and 100%, respectively. The differences in PM 2.5 concentrations between Base and S1RN can estimate the effects of Nr emission reductions. Third, a group of sensitivity simulations (denoted as S2RN, N = 30, 60, 80, and 100), similar to S1RN, but only reduces NO x emissions. Fourth, another group of sensitivity simulations (denoted as S3RN, N = 30, 60, 80, and 100), similar to S1RN, but only reduces NH 3 emissions. The comparison of PM 2.5 changes between S2RN and S3RN then quantifies the respective effectiveness of NO x and NH 3 abatement. For all simulations, typical months for the four seasons (January, April, July, and October) after a 3-day spin-up for initialization are simulated to represent yearly results due to limited computing resources.

Health-impact of Nr emission on PM 2.5
We assess the PM 2.5 -related chronic health impacts through the Global Exposure Mortality Model (GEMM) 58 . It develops a PM 2.5 -mortality hazard ratio function according to cohort studies of worldwide outdoor air pollution, and has been widely used in recent studies 59,60 . This concentration-response function-based method focuses on total PM 2.5 mass without assessing individual PM 2.5 components for which evidence is limited 9 , corresponding with the GBD study 1 . The total health burden of long-term PM 2.5 exposure is attributed to noncommunicable diseases and lower respiratory infections (NCD and LRI). PM 2.5 -related premature deaths (ΔMort) for adults (≥25 years) with age groups in 5-year intervals from 25 to greater than 85 are calculated by the following formulas: Þ=ð1 + expðÀ z À μ υ ÞÞÞ, z = maxð0, c À 2:4Þ where RR i is the relative risk of NCD or LRI for age group i (i = 1, 2,…,12), which means the contribution of PM 2.5 pollution to the baseline mortality rate; c is ambient annual PM 2.5 concentrations, exp is the natural exponential function, and θ, α, μ and υ are parameters that determine the shape of relative risk in GEMM and are specified for each age group. The PM 2.5 threshold is 2.4 μg·m -3 , below which no impact occurs. Base i is the baseline mortality rate of NCD or LRI for age group i, obtained from the Global Burden of Disease Study of 2015, and Pop i is the gridded population within age group i, derived from the Gridded Population of the World version 4.11 (GPWv4) dataset. We further use the Monte Carlo method to provide the 95% confidence interval (CI) of deaths through ten thousand-time estimates.
Indicators of Nr control for PM 2.5 mitigation Here, we apply a mass-based indicator of instant efficiency to quantify the effectiveness of Nr controls in reducing total PM 2.5 concentrations, and then use a molar-based indicator of G ratio to explain changes in the effectiveness of PM 2.5 mitigation. We calculate the efficiency of Nr emission controls based on the sensitivity simulations following the definition in Liu's (2021) 26 . The instant efficiency is defined as: G ratio is applied to diagnose the availability of NH 3 in the air and to analyze the chemical regime of SIAs formation 25 . We calculate the G ratio using the equations below. ] are the molar concentrations (in unit of µmol·m −3 ). Values of the G ratio below 1 mean that ammonia is insufficient to neutralize all H 2 SO 4 and total nitrate, indicating an NH 3 -limited chemical regime where SIAs formation is limited by the availability of NH 3 35 . In contrast, values of the G ratio above 1 mean that ammonia is sufficient to neutralize total nitrate, which characterizes a HNO 3 -limited chemical regime where SIAs formation is limited by the availability of HNO 3 . The G ratio of 1 means that changes (in mol units) in NH 3 and NO x emissions can result in similar PM 2.5 changes. We note, that such diagnoses concerning SIAs formation to NH 3 and to HNO 3 availability are invalid for high temperature and low relative humidity as little ammonium nitrate aerosol is present 25 .

Diagnostic diagram for Nr control pathways
The diagnostic diagram is developed for evaluating Nr control pathways targeting PM 2.5 abatement (Fig. 5). We first calculate PM 2.5 concentrations on each 10% Nr (NO x or NH 3 ) emission scenario (the white circle symbols in the diagnostic diagram) through a shape-preserving piecewise cubic spline interpolation among the 13 sets of simulated regional mean PM 2.5 concentrations (the black circle symbols in the diagnostic diagram) to obtain PM 2.5 isopleths. The isopleth gradients (the blue arrows in the diagnostic diagram) are then calculated as Eq. 7 to represent the effectiveness of PM 2.5 reductions.
∇½PM 2:5 = ∂½PM 2:5 ∂x ×ĩ + ∂½PM 2:5 ∂y ×j = β NH3 ×ĩ + β NOx ×j ð7Þ Here x and y axes represent the strengths of the NH 3 and NO x emission controls, respectively. i and j are unit vectors in the x-direction and y-direction, respectively. ∂PM 2.5 /∂x is the gradient in the x-direction showing instant efficiency from NH 3 controls. ∂PM 2.5 /∂y is the gradient in the y-direction showing instant efficiency from NO x controls. The effectiveness diagnostic diagram can illustrate the total PM 2.5 declines by isopleths, the combined instant efficiency on PM 2.5 abatement by the size of arrows, and the relative efficiency between NH 3 and NO x by the direction of arrows. Therefore, the optimal pathway for effective PM 2.5 declines can be found by following the isopleth gradients.

Data availability
Surface chemical measurements in Europe are obtained from the air quality database of the European Environment Agency (EEA, https:// www.eea.europa.eu/data-and-maps/data/aqereporting-9).
Meteorological observations are available from the National Climatic Data Center (NCDC, https://ncdc.noaa.gov/isd/data-access). Gridded population and demographic characteristics are derived from the Gridded Population of the World version 4.11 (GPWv4) dataset (https:// doi.org/10.7927/H4PN93PB, https://doi.org/10.7927/H46M34XX). The baseline mortality rate of noncommunicable diseases and lower respiratory infections are obtained from the Global Burden of Disease Study (https://vizhub.healthdata.org/gbd-results/). The anthropogenic emission inventory and emission control costs are available from the corresponding author on request. The data and modeling outputs generated in this study have been deposited at https://doi.org/10.5281/ zenodo.7934101 61 and are openly accessible.

Code availability
The codes of WRF-Chem version 4.0.3 are available at https://github. com/wrf-model/WRF/releases/tag/v4.0.3. Codes for calculations and data processing are written in MATLAB and are available from the corresponding author upon request.